Babaco is a fast-growing herbaceous shrub with great commercial potential because of the organoleptic properties of its fruit. Babaco mosaic virus (BabMV) is a potexvirus in the family Alphaflexiviridae affecting babaco in all the provinces that produce this crop in Ecuador. BabMV was recently described but it has been affecting babaco for decades and, since many potexviruses are serologically indistinguishable, it may have been previously misidentified as papaya mosaic virus. Based on the coat protein (CP) gene, we aimed to study the distribution and epidemiological patterns of BabMV in babaco and chamburo over the years and to model its three-dimensional structure. Sequences of the CP were obtained from thirty-six isolates from plants collected in the main babaco-producing provinces of Ecuador between 2016 and 2021. The evolution rate of BabMV was estimated at 1.21 × 10−3 nucleotide substitutions site−1 year−1 and a time of origin of the most recent common ancestor around 1958.80. From molecular dynamics simulations, compared to other proteins of BabMV—RDRP, TGB1, and Alkb domain—the CP exhibited a higher flexibility with the C and N terminals as the most flexible regions. The reconstructed viral distribution provides dispersion patterns which have implications for control approaches of BabMV.